B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations

A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.Comment: 27 pages, 30 figure

Surgery of spline-type and molecular frames

We prove a result about producing new frames for general spline-type spaces by piecing together portions of known frames. Using spline-type spaces as models for the range of certain integral transforms, we obtain results for time-frequency decompositions and sampling.Comment: 34 pages. Corrected typo

Exploratory Analysis of Benchmark Experiments -- An Interactive Approach

The analysis of benchmark experiments consists in a large part of exploratory methods, especially visualizations. In Eugster et al. [2008] we presented a comprehensive toolbox including the bench plot. This plot visualizes the behavior of the algorithms on the individual drawn learning and test samples according to specific performance measures. In this paper we show an interactive version of the bench plot can easily uncover details and relations unseen with the static version